Ternary Parameters Research Articles

Thermodynamic Modeling of Ni-C, Co-C, and Ni-Co-C Liquid Alloys Using the Modified Quasichemical Model

The strong interactions between the metallic elements and C in liquid Ni, Co, and Ni-Co alloys have been thermodynamically analyzed. The liquid solution properties in Ni-C and Co-C systems showed significant asymmetry because of the short-range ordering of C exhibited in the liquid solution. Using the modified quasichemical model in the pair approximation, the Ni-C and Co-C systems were re-optimized to simultaneously reproduce the present experimental results of the C solubility and the reported thermodynamic properties in the liquid phases. In particular, the partial enthalpy data of C in liquid Ni and Co alloys were considered for the first time on the thermodynamic assessment of Ni-C and Co-C liquid solutions. The asymmetric interpolation method was introduced to evaluate the Gibbs free energy in the ternary system based on the binary Gibbs free energies in the Ni-C and Co-C systems. The C solubility data measured in the ternary Ni-Co-C alloy melt over a wide Co concentration range were successfully reproduced without any additional ternary model parameter by considering the short-range ordering of C.

Critical evaluation and thermodynamic modeling of the Fe–P and Fe–C–P system

Phosphorus is known to be a strongly segregating element in steel; even small amounts influence the solidification phenomena and product quality during casting processes. In order to provide an accurate prediction tool for process control in steelmaking, a CALPHAD-type thermodynamic optimization of the Fe–C–P system was performed including modeling of the binary Fe–P subsystem. The liquid phase was modeled using the Modified Quasichemical Model (MQM) in the pair approximation, which generally yields better results for strong short-range ordering (SRO) tendency in the solution. The solid bcc and fcc solutions were described using the Compound Energy Formalism (CEF). In addition, ab-initio calculations were performed to estimate the enthalpies of formation of the corresponding end-member for fcc and bcc, respectively. The phosphides Fe3P, Fe2P and FeP were treated as stoichiometric compounds. Higher order phosphides were not considered, since there is no reliable experimental information available in literature. The present model successfully reproduces most of the literature data within the experimental uncertainty in the Fe–C–P system without introducing a ternary parameter for the liquid phase. Compared with previous thermodynamic assessments, the agreement with recently published thermal analysis measurements of Fe–P and Fe–C–P alloys is significantly improved.

Excess molar volumes and excess isentropic Compressibilities of ternary [Bmim][BF4]-[Emim][BF4]-Cyclopentanone or cyclohexanone mixtures at various temperatures t = (293.15–308.15) K

Abstract The current study focuses on excess molar volumes, V 123 E and excess isentropic compressibilities, ( κ S E ) 123 of ternary mixtures comprise of 1‑butyl‑3-methylimidazolium tetrafluoroborate, 1-ethyl-3-methylimidazolium tetrafluoroborate, cyclopentanone and cyclohexanone. The objective of the study is to obtain information about the state of components in pure state along with the molecular interactions operating among the constituent molecules. Mixtures under study with different compositions have been prepared by mass and their densities, ρ123 and speed of sound, u123 values have been measured at (293.15 to 308.15) K with 5 K interval and 0.1 MPa. The calculated excess molar volumes, V 123 E and excess isentropic compressibilities, ( κ S E ) 123 values (using their measured densities and speed of sound data) have been satisfactorily correlated using Redlich-Kister polynomial equation. The ternary adjustable parameters and standard deviations between experimental and calculated values have also been reported. The results have been discussed in terms of Graph theory to obtain the expressions of V 123 E and ( κ S E ) 123 values. The theoretical predicted V 123 E and ( κ S E ) 123 values are comparable to experimental data which in turn support the various assumptions made for the various processes involved in (1 + 2 + 3) mixtures formation.

A Two-Parameter Theoretical Model for Predicting the Activity and Osmotic Coefficients of Aqueous Electrolyte Solutions

A thermodynamic model of electrolyte solutions is proposed. The model consists of a long-range term expressed by the Pitzer–Debye–Huckel equation (PDH) and a short-range term expressed by the molecular interaction volume model (MIVM). The new model was fitted with 39 different types of single electrolyte systems and was compared with the Pitzer equation, and the mean standard deviation (SD) and the mean average relative deviation (ARD%) are 0.0264, 0.0040 and 2.09%, 0.40%, respectively. Meanwhile, the physical meaning of the two electrolyte-specific interaction parameters ( $$B_{ca,s}$$ and $$B_{s,ca}$$ ) of the new model is also discussed. By further comparison with the Pitzer equation and a state-of-the-art model, eUNIQUAC-NRF, the new model exhibits relatively robust extrapolation capability, and also shows the potential ability to predict the activity coefficients of individual ions. In addition, only using binary parameters to predict 29 different types of ternary systems, the overall prediction results of the new model are slightly better than those of the Pitzer equation, and the mean SD and ARD% are 0.0288, 0.0396 and 2.88%, 3.81%, respectively. For some cases involving Rb and Cs, the Pitzer equation needs two ternary adjustable parameters ( $$\theta$$ and $$\psi$$ ) to achieve the prediction accuracy of the new model. Furthermore, we also compared the predictions of the new model with the eUNIQUAC-NRF model for several ternary systems; the new model also shows better performance, and its overall prediction accuracy was about twice that of the eUNIQUAC-NRF model, with the average SD and ARD% values being 0.0261, 0.0546 and 2.63%, 5.80%, respectively.

Guaranteed storage and stabilization of desired binary periodic orbits in three-layer dynamic binary neural networks

This paper presents three-layer dynamic binary neural networks characterized by ternary connection parameters and the signum activation function. The dynamics is described by a difference equation of binary state variables. Depending on the parameters, the network can generate various binary periodic orbits. We give two main theoretical results. First, when a desired periodic orbit is given, we can set the parameters that guarantee storage and local stability of the periodic orbit. The stability is related to error correction of various binary signals in engineering applications. Second, if a part of the connection parameters becomes zero then stability of the periodic orbit becomes very strong. In this case, all the initial states fall directly into the periodic orbit.

Thermodynamic description, hardness and electrical conductivity of the Bi–Ni–Zn system: Experiment and modeling

Selected ternary systems are chosen due to the significant interest of nickel alloys in the different industry such as electronic, chemical, automotive, marine etc. Chosen ternary system up to this paper has not been studied. The ternary system Bi–Ni–Zn has been experimentally and analytically tested. Temperatures of phase transformation were determined by differential thermal analysis (DTA) on 12 ternary samples. Obtained results by DTA test were compared with calculated vertical sections Bi–NiZn, Ni–BiZn and Zn–BiNi. Hardness and electrical conductivity were measured for some alloys. By using experimental results of hardness and electrical conductivity tests, mathematical model has been proposed for calculation of those properties along all composition ranges. Composition of alloys and phases in alloys annealed at 400 and 700 °C were determined by scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS). Obtained results by EDS were compared with calculated isothermal sections at 400 and 700 °C. X-ray powder diffraction (XRD) tests were used for phase identification in all ternary samples. Used analytical method was Calphad method. Calculation of phase diagrams (three vertical sections and two isothermal sections) was performed by using thermodynamic parameters for constitutive binary systems. Good agreements between calculated phase diagrams and experimental data have been reached without introducing ternary thermodynamic parameters. Based on this conclusion liquidus projection and invariant reaction were calculated without additional experimental tests.

Solubility of ammonium fluoride in aqueous sodium fluoride solutions of various concentrations from dilute to saturated at 298.15 K for fluorine recovery from wet-process phosphoric acid

Recovery of fluorine from wet-process phosphoric acid (WPA) to produce ammonium fluoride (NH4F) and sodium fluoride (NaF) provides an environmentally-friendly route to purify WPA and produce high value-added fluoride salt. The solubility data and the related electrolyte thermodynamics are essential for a rational separation design of pure NH4F from aqueous NaF solution by crystallization. In this contribution, the solubilities of NH4F in aqueous NaF solutions of different concentrations from dilute to saturated were systematically measured at 298.15 K using a dynamic synthesis method. Experimental results show that the presence of NaF in the solution could significantly decrease the solubility of NH4F due to the common-ion effect which was decreased by 72.4% when the molality of NaF was only around 0.015 mol/kg. The data can be used to determine the yield of NH4F and liquid composition in the vacuum evaporative crystallization of NH4F. The mean activity coefficients of NH4F at saturation were determined from the experimental solubility data and then correlated with the extended Debye-Hükel equation and the Pitzer model. With four adjustable parameters, both models are able to accurately calculate the experimental data over a wide range of salt concentrations. The average relative deviations between the experimental and calculated logarithm of mean activity coefficients of NH4F from the two models are 1.43% and 2.29%, respectively. The binary and ternary ionic parameters for the Pitzer model are found to be concentration dependent and the correlations of them as functions of ionic strength are proposed.

Experimental examination and thermodynamic description of the ternary Bi-Ge-Ga,Zn systems

Due to the wide application of systems based on germanium ternary Bi-Ga-Ge and Bi-Ge-Zn systems were experimentally tested in this study. Used experimental techniques were scanning electron microscope with energy dispersive spectroscopy (SEM-EDS), x-ray diffraction (XRD) and differential thermal analysis (DTA). Three groups of samples were prepared and tested. Alloys were from two isothermal sections at 100 and 300 °C and three vertical sections. Obtained results of experimental tests were compared with predicted phase diagrams. Comparison of EDS and DTA results with calculated phase diagrams of the ternary Bi-Ga-Ge system results in good agreement. While for Bi-Ge-Zn was necessary to introduce new ternary parameters. Introduced ternary parameters were based on experimental results from this study. The thermodynamic descriptions of the ternary Bi-Ga-Ge and Bi-Ge-Zn systems have been developed by using CALPHAD method. Reasonable agreement between experimental data and the calculated phase diagrams has been reached for both ternary Bi-Ga-Ge and Bi-Ge-Zn systems. The liquid projection and invariant equilibria have been calculated by using obtained thermodynamic parameters.

Experimental Examination and Thermodynamic Description of the Ternary Bi-Ge-In and -Sn Systems

In the present study, ternary Bi-Ge-In and Bi-Ge-Sn systems were experimentally investigated using differential thermal analysis (DTA), scanning electron microscopy with energy dispersive spectroscopy (SEM–EDS) and x-ray diffraction. The results of experimental investigation were compared with thermodynamically predicted phase diagrams. Temperatures of phase transformations, determined by DTA, were compared with the calculated vertical sections (three vertical sections per ternary systems were investigated) and a close agreement was obtained. The results of EDS analysis were compared with the calculated isothermal sections. Phase compositions of co-existing phases, determined by EDS analysis, were found to support the corresponding calculated phase compositions quite well. Based on the observed overall good agreement between the results of experiments and thermodynamic calculations, it was concluded that fairly accurate descriptions of the phase diagrams of ternary Bi-Ge-In and Bi-Ge-Sn systems can be obtained without the introduction of ternary thermodynamic parameters. By using the proposed thermodynamic datasets, liquidus projections and invariant reactions have been predicted for both the investigated ternary systems.

Using DTA/DSC data for assessment of the Toop and Muggianu predictive models for the Ag–Au–In ternary

The relative performance of the Muggianu and Toop methods of preliminary prediction of thermodynamic properties of solution phases is tested using Ag–Au–In ternary as a model system, which was recently studied by the present authors. The temperatures of solids, monovariant reaction (where appropriate) and liquids, as well as the heat of melting of solid solutions, were measured by DTA/DSC for five ternary samples. Different extrapolation models generate very different descriptions of phase equilibria. However, accounting for ternary interactions brings all the results into moderately close agreement. In both methods, the values of ternary parameters for liquid phase are more negative than for solid phases (about twice in modulo in Muggianu one and up to ten times in Toop case). This implies the stabilization of liquid in central concentration region. Neither predictive model captures this without accounting for ternary interactions.

Theoretical confirmation of an established experimental phase diagram of ternary system (Cu(SO4)–Zn(SO4)–H2O) at 25 °C: Pitzer parameters determination

The isotherm phase diagram of the ternary system (Cu(SO4)–Zn(SO4)–H2O) was firstly established at 25°C using a synthetic method of conductivity measurement. Then, we made use of volumetric dosing, in order to identify solid phases. The obtained isotherm has revealed the presence of two solid phases that having a stable equilibrium with the liquid phase, which are Cu(SO4)·5H2O, and the Zn(SO4)·7H2O. This study was confirmed numerically while going through the calculation of the binary and ternary Pitzer parameters for the studied salts through a Nelder Mead simplex algorithm. Indeed, the comparison of these with the bibliographic data has confirmed the accuracy of our experimental results.

Water Activity and Solubility of the System MgCl2–RbCl–H2O at 323.15 K

The water activities of the MgCl2–RbCl–H2O ternary system and its sub-binary systems have been measured with the isopiestic method at 323.15 K. The measured water activities for the MgCl2–H2O and RbCl–H2O sub-binary systems agree well with the results reported in literature. The measured equal water activity lines of the MgCl2–RbCl–H2O ternary system are not straight lines, which means the mixing behavior of the solutions do not obey Zdanovskii’s rule. The solubility of the MgCl2–RbCl–H2O ternary system has been determined with the Flow-Cloud-Point method at 323.15 K, and the measured results are roughly consistent with values reported in the literature. The Pitzer model was selected to correlate the water activity and solubility data measured in this work. The predicted water activities and solubility isotherm for the MgCl2–RbCl–H2O ternary system at 323.15 K, with binary solution parameters only, both deviated from the experiment values. The ternary solution Pitzer model parameters were obtained by fitting the measured water activities in the ternary system. The water activities and solubility isotherms of the MgCl2–RbCl–H2O ternary system at 323.15 K were calculated including both binary and ternary solution parameters. The calculated water activities are consistent with the experimental values. The calculated solubility isotherms are roughly consistent with experiment values, except they deviate somewhat in the RbCl crystallization region.

Solubility measurements in Na-F-CO3-HCO3-H2O system at (308.15 and 323.15) K and development of a Pitzer-based equilibrium model for the Na-F-Cl-SO4-CO3-HCO3-H2O system

Fluoride is highly related to human health. Thermodynamic equilibrium models can used as be powerful predictive and interpretive tools to evaluate its potential hazards. A few works have ever been conducted to deal with fluoride involved aqueous solutions. However, bicarbonate and sulfate, which have a positive relationship with the concentration of fluoride in aqueous solutions, have not been evaluated. In this work, the solubilities in the NaF-Na2CO3-H2O system and the NaF-Na2CO3-NaHCO3-H2O system were determined with the isothermal dissolution method at (308.15 and 323.15) K and atmosphere pressure. Using this set of experimental data and those from the literature, a thermodynamic equilibrium model in the mixed system Na-F-CO3-HCO3-H2O was developed based on the Pitzer specific interaction model. The model gave very good agreement with the experimental solubility data. For the Na-F-SO4-H2O system, the solubility products of the double salt NaF·Na2SO4 and ternary Pitzer parameters were determined from experimental data available in the literature. Combining the parameters evaluated in this work and those from previous literature, a solid-liquid equilibrium model was developed for the Na-F-Cl-SO4-CO3-HCO3-H2O system at temperatures up to 363.15 K. The model was validated by comparing solubility predictions with experimental data given in literature, and those were not used in the parameterization process.

Excess molar volumes and excess isentropic compressibilities of mixtures containing lactam, cyclic ethers and cyclic alkanones

Abstract Measurements of densities, ρ, ρ123 and speeds of sound, u, u123 of binary 1,3-dioxolane (1) + 1,4-dioxane (2) and ternary 1,3-dioxolane (1) + N-methylpyrrolidi-2-one or 1,4-dioxane (2) + cyclohexanone or cycloheptanone (3) mixtures have been carried out over the entire range of mole fraction at 293.15, 298.15, 303.15, 308.15 K and atmospheric pressure. The excess molar volumes, V 12 E , V 123 E and excess isentropic compressiblities, ( κ S E ) 12 , ( κ S E ) 123 have been determined from experimental data. The V 123 E and ( κ S E ) 123 data for 1,3-dioxolane (1) + N-methylpyrrolidin-2-one (2) + cyclohexanone or cycloheptanone (3) and 1,3-dioxolane (1) + 1,4-dioxane (2) + cycloheptanone (3) mixture are negative over entire composition of (1) and (2). While V 123 E for 1,3-dioxolane (1) + 1,4-dioxane (2) + cyclohexanone (3) are positive across full range of compositions of (1) and (2); the sign and magnitude of ( κ S E ) 123 values vary with change in composition of the constituent molecules. The V 12 E , V 123 E and ( κ S E ) 12 , ( κ S E ) 123 data have been fitted to Redlich-Kister equation to determine binary, ternary adjustable parameters and standard deviations. The V 123 E and ( κ S E ) 123 data have been analyzed in terms of Graph Theory. It has been observed that Graph theory correctly predicts the sign as well as magnitude of V 123 E and ( κ S E ) 123 data of the studied ternary mixtures.

Excess heat capacities and excess molar enthalpies of the mixtures containing tetrahydropyran, piperidine and cyclic alkanones

In the present study, molar heat capacities, $$\left( {C_{\text{P}}^{{}} } \right)_{123}$$ , at T/K = 293.15–308.15 K with 5 K interval and excess molar enthalpies, $$H_{ 1 2 3}^{\text{E}}$$ , at T/K = 308.15 for ternary tetrahydropyran (1) + piperidine (2) + cyclohexanone or cycloheptanone (3) and molar heat capacities, $$(C_{\text{P}}^{{}} )_{12}$$ , for binary tetrahydropyran (1) + piperidine (2) mixture at T/K = 293.15, 298.15, 303.15 and 308.15 have been determined as a function of composition using microdifferential scanning calorimeter. The $$\left( {C_{\text{P}}^{\text{E}} } \right)_{123}$$ , $$H_{123}^{\text{E}}$$ and $$(C_{\text{P}}^{\text{E}} )_{12}$$ data have been fitted to Redlich–Kister equation to predict ternary and binary adjustable parameters along with standard deviation in the measured properties. The observed $$\left( {C_{\text{P}}^{\text{E}} } \right)_{123}$$ , $$H_{123}^{\text{E}}$$ data have been tested in terms of graph theory which in turns deals with the topology of the constituent molecules. It has been observed that $$\left( {C_{\text{P}}^{\text{E}} } \right)_{123}$$ and $$H_{123}^{\text{E}}$$ values estimated by graph theory are comparable with the experimental data.

Excess molar volumes and excess isentropic compressibilities of liquid mixtures formed by tetrahydropyran, piperidine and cyclic ketones at temperature from 293.15 to 308.15 K.

The densities, ρ, ρ123 and speeds of sound, u, u123 of binary Tetrahydropyran (1)+Piperidine (2) and ternary Tetrahydropyran (1)+Piperidine (2)+Cyclohexanone or Cycloheptanone (3) mixtures have been measured over the whole range of mole fraction at 293.15, 298.15, 303.15, 308.15K and atmospheric pressure. The observed data have been utilized to determine excess molar volumes, (VE)12, V123E and excess isentropic compressibilities, (κSE)12, (κSE)123 for the binary and ternary liquid mixtures respectively. The (VE)12, V123E and (κSE)12, (κSE)123 data have been fitted to Redlich-Kister equation to determine binary as well as ternary adjustable parameters along with standard deviations. The Moelywn-Huggins concept of interaction between the surfaces of the binary mixture constituents has been extended (Graph theory) to evaluate excess molar volumes and excess isentropic compressibilities of ternary mixtures using the concept of connectivity parameter of third degree of molecules, 3ξ (which deals with the topology of the constituents in pure and mixed state) to obtain an expression that describe well the measured data.

Thermodynamic evaluation of the BaO-CaO-YO1.5 system

A series of experiments were performed to study the solid solubility of CaO in BaY2O4, and the observed results were then adopted to the present thermodynamic evaluation to derive a set of thermodynamic database for the BaO-CaO-YO1.5 system. The database was constructed by the CALPHAD method where the binary parameters from the BaO-CaO and CaO-YO1.5 systems were presently optimized, those from the BaO-YO1.5 system were simulated by our previous assessments, and only limited amount of ternary parameters were introduced. All the model parameters were emanated from the Bragg-Williams approximation where the liquid and terminal solid-solution phases were treated by the one-sublattice model, and two ternary intermediate phases, named BCY (BaCa2Y6O12) and BaY2O4, were described by the three-sublattice and two-sublattice models, respectively. Good agreement between the experimental data and the calculated results demonstrates that the present thermodynamic database is self-consistent and credible and able to be used to design novel refractory.

Densities and excess volumes of aqueous monoethanolamine and diisopropanolamine systems at atmospheric pressure from 303.15 K to 333.15 K

The densities of water+monoethanolamine (MEA), water+diisopropanolamine (DIPA), DIPA+MEA binary systems and water+DIPA+MEA ternary system were measured over the full range of composition at temperatures from 303.15 K to 333.15 K by using an Anton Paar digital vibrating tube density meter (DMA4500). The experimental excess volumes were obtained from the experimental density results and fitted using the Redlich-Kister-Muggianu expression. The parameters obtained from the binary excess volume data were used for the correlation of ternary system with one additional ternary parameter for each isotherm. All investigated binary and ternary systems are completely miscible, because the values of excess volume are negative under the examined conditions.

Database development and Calphad calculations for high entropy alloys: Challenges, strategies, and tips

The development of a reliable multicomponent thermodynamic database for high entropy alloys (HEAs) is a daunting task and it faces new challenges comparing to the development of databases for conventional single principal element alloys, such as the assessment of a large number of ternary systems, the proper estimation of phase stability within metastable compositional and temperature ranges, and the reasonable extrapolation into higher order systems. We have recently established a thermodynamic database (TCHEA1) especially for HEAs within a 15-element framework. This work highlights the usage of high throughput density functional theory (DFT) calculations for validating and refining the binary and ternary parameters of the solid solution phases, and having a more reliable extrapolation into metastable regions and higher order systems. TCHEA1 consists of 105 binaries and 200 ternaries and contains nearly all the stable solution phases and intermetallic compounds in each of the assessed systems. Together with Thermo-Calc, this database enables us to predict the stability of the desired multicomponent solid solution relative to intermetallic compounds and other solid solutions. Calculation examples are presented not only for case studies but also for bridging the knowledge gap between Calphadian and people who do not have a background of the Calphad approach.

Effect of Tin on the Phase Transformations of Cast Irons

Copper, manganese and essentially tin are used as alloying elements for obtaining cast irons with a fully pearlitic matrix in the as-cast state. Addition of tin, at a level of about 0.10-0.15 mass%, seems to be the only practical way for avoiding growth of ferrite in the stable eutectoid reaction and to fully transform the matrix of the material to pearlite in the metastable eutectoid system. While the role of copper and manganese has been previously rationalized, the way tin affects the eutectoid transformation in cast irons is still a matter of debate. The present work makes use of an assessment of the Fe-Sn system and of experimental data in the Fe-C-Sn system to evaluate the effect of tin on phase equilibria in this latter system. One ternary parameter is estimated and the resulting modification is applied to literature data on Fe-CSi- Sn equilibria. Finally, solid-state phase transformation temperatures are calculated and used to discuss experimental information dealing with pearlitic cast irons. It is proposed that pearlite formation in Sn-bearing cast irons is associated to the transient formation of a Fe3SnC compound which has an ordered FCC structure.